Confusing uage of present perfect infinitive where past perfect should be used

You can't have a conjugated form after "to". "Had" has to have a subject in the third person (he, she, it, this man, a person, etc.); the subject of "is" is "he"; then there is no subject for "had"; that is because "had" is wrong here, you must have the bare infinitive: "have".

You also have to keep in mind the usual construction in the passive for "think".

• to be thought to be sth/sb (OALD, 1)

Is only conjugated the first occurrence of "to be". When you state a fact about events, situations, people and so on and that this fact is still valid in the present , the plain infinitive is used.

• They are thought to be taking this seriously.

If the fact is a thing of the past, then you use the perfect infinitive.

• They are all thought to have been killed in the last war but nothing is less sure.

That is the case of your sentence: he was depressed in the past (at least some people think he was); it is a thing of the past.